To estimate square roots, we need to find the perfect squares that are closest to the number inside the square root. A perfect square is a number like 1, 4, 9, 16, 25, etc., which comes from multiplying a whole number by itself (e.g., $5 \times 5 = 25$).
Here is the step-by-step logic for each problem:
1. $\sqrt{5}$
* Think of perfect squares near 5.
* $2^2 = 4$ and $3^2 = 9$.
* Since 5 is between 4 and 9, $\sqrt{5}$ is between
2 and
3.
2. $\sqrt{12}$
* Think of perfect squares near 12.
* $3^2 = 9$ and $4^2 = 16$.
* Since 12 is between 9 and 16, $\sqrt{12}$ is between
3 and
4.
3. $\sqrt{34}$
* Think of perfect squares near 34.
* $5^2 = 25$ and $6^2 = 36$.
* Since 34 is between 25 and 36, $\sqrt{34}$ is between
5 and
6.
4. $\sqrt{23}$
* Think of perfect squares near 23.
* $4^2 = 16$ and $5^2 = 25$.
* Since 23 is between 16 and 25, $\sqrt{23}$ is between
4 and
5.
5. $\sqrt{101}$
* Think of perfect squares near 101.
* $10^2 = 100$ and $11^2 = 121$.
* Since 101 is between 100 and 121, $\sqrt{101}$ is between
10 and
11.
6. $\sqrt{60}$
* Think of perfect squares near 60.
* $7^2 = 49$ and $8^2 = 64$.
* Since 60 is between 49 and 64, $\sqrt{60}$ is between
7 and
8.
7. $\sqrt{41}$
* Think of perfect squares near 41.
* $6^2 = 36$ and $7^2 = 49$.
* Since 41 is between 36 and 49, $\sqrt{41}$ is between
6 and
7.
8. $\sqrt{96}$
* Think of perfect squares near 96.
* $9^2 = 81$ and $10^2 = 100$.
* Since 96 is between 81 and 100, $\sqrt{96}$ is between
9 and
10.
9. $\sqrt{125}$
* Think of perfect squares near 125.
* $11^2 = 121$ and $12^2 = 144$.
* Since 125 is between 121 and 144, $\sqrt{125}$ is between
11 and
12.
10. $\sqrt{116}$
* Think of perfect squares near 116.
* $10^2 = 100$ and $11^2 = 121$.
* Since 116 is between 100 and 121, $\sqrt{116}$ is between
10 and
11.
11. $\sqrt{79}$
* Think of perfect squares near 79.
* $8^2 = 64$ and $9^2 = 81$.
* Since 79 is between 64 and 81, $\sqrt{79}$ is between
8 and
9.
12. $\sqrt{42}$
* Think of perfect squares near 42.
* $6^2 = 36$ and $7^2 = 49$.
* Since 42 is between 36 and 49, $\sqrt{42}$ is between
6 and
7.
Final Answer:
1. 2 and 3
2. 3 and 4
3. 5 and 6
4. 4 and 5
5. 10 and 11
6. 7 and 8
7. 6 and 7
8. 9 and 10
9. 11 and 12
10. 10 and 11
11. 8 and 9
12. 6 and 7
Parent Tip: Review the logic above to help your child master the concept of estimate square root worksheet.
